(Solved): This is applied numerical method subject. Hi. Please help solve question i-iv, a detailed steps and ...

This is applied numerical method subject.

Hi. Please help solve question i-iv, a detailed steps and solution will be much appreciated. Thank you.

You are asked to design a soft closing sliding door. As shown in the figure below, this device consists of a spring and an air damper where one end is fixed to the wall and another end is fixed to the door. This device will close the door automatically when someone releases the door with some distance from wall. Spring Damper Door Distance from wall x=0 Let the movement of the door after touching the soft closing device represented by a second order motion equation as in below: d²x dx mdt² + cdt + kx Where, x is the distance of the door from the wall with x = 0 at the wall m is the mass of the door C is the damping capacity k is the spring constant Given the spring constant, k is 10 N/m, damping coefficient, C is 8 N s/m, mass of the door, m is 2 kg and the door is released from static at the distance from wall equal to 0.5 meter. i) Convert the given second-order equation in first order equations. (1.5 M) (1.0 M) ii) Identify all the initial or boundary conditions for the given system. iii) Suggest a first order accuracy numerical method to solve the first order equations derived in i). Hence, find the distance of x at t = 0.6 s using a step size of 0.2. (5.0 M) iv) Given that the exact answer for x at t = 0.6 s is 0.29436 m, compare this with your answer in iii) by calculating the percentage error. Suggest two methods to improve the accuracy of the answer in iii). (2.5 M)